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Question:

Prove that: sin2(π/6) + cos2(π/3) - tan2(π/4) = 1/2

Solution:

L.H.S = sin2(π/6) + cos2(π/3) - tan2(π/4) = (1/2)² + (1/2)² - 1 = 1/4 + 1/4 - 1 = 1/2
Therefore, L.H.S = R.H.S
Hence proved.